The difference in SD is slightly over 1 part in 10,000, which is close enough for me.

(Fred: feel free to add this to your tidbits page, if you want.)

EDIT: removed a debugging "-write mean.png" from the single-command convert.

EDIT2: if the input image is fully opaque for the single-command convert, the "CopyOpacity" is wrong so the "SD of opaque" is wrong. If "convert %INFILE% -format "%[opaque]" info:" returns "true", don't use this to find the SD of opaque pixels.